When electromagnetic (em) radiation propagates from a first medium into a second medium, it is subject to the effects of optical refraction and Fresnel reflection, arising from any difference in the refractive index of the two media at the wavelength of the em-wave. With reference to FIG. 1(a), the magnitude of the optical refraction experienced by the em-wave in propagating from a first medium of refractive index n l into a second medium of refractive index n2 is described mathematically by: n1 sin(α1)=n2·sin(α2), where a, is the angle within the first medium at which the em-wave strikes the interface between the two media, and α2 is the angle within the second medium at which the em-wave transmitted through the interface leaves the interface, each angle being measured relative to the normal or perpendicular to the interface.
When n1 is greater than n2, then there exists some angle α for which when α1 equals α then α2 equals 90 degrees. When this condition exists the em-wave is guided along a direction parallel to the interface and not transmitted into the second medium. Further, when α1 is greater than α, the em-wave is totally reflected at the interface resulting in the em-wave being returned into the first medium rather than being transmitted into the second medium, this being the principle of total internal reflection and used widely in fiber optic devices. While advantageous in fibre optic devices, the effect of total internal reflection can be detrimental to devices where transmission from a first medium of high refractive index into a second medium of low refractive index is desired.
With reference to FIG. 1(b), the magnitude of the component of the em-wave reflected from an interface between a first medium of refractive index n1 and a second medium of refractive index n2 at or near normal incidence is approximated and described mathematically by: R=(n1-n2)2/(n1=n2)2. When the difference between n1 and n2 is large, it is easily seen that the magnitude of the reflected component of the em-wave also becomes large. For example if n1, is five and n2 is one, then R is close to 45%. In many optical systems this is a detrimental loss and so means are sought to circumvent or mitigate the effect.
One solution, as shown in FIG. 1(c), is to insert an additional layer of material of intermediate refractive index (n3), i.e. n2 is less than n3 that is less than n1, between the first and second media. Excluding any affect due to interference between transmitted and reflected components, the total transmission is then given by the product of the transmissions of the em-wave propagating firstly from medium 1 into medium 3 then medium 3 into medium 2. For example, if n3 equals three and n1 and n2 are as above, the total loss is reduced to close to 12%. If the interfaces between the media are substantially parallel and the intermediate layer made appropriately thin (typically a quarter of the wavelength of the em-wave) then it is the case that interference effects can be used to further reduce the magnitude of the reflected component to close to zero, this being the principle of operation of single-layer anti-reflection coatings.
A particular example of where it is advantageous to use a device of intermediate refractive index to improve coupling of an em-wave between media of high and low refractive index is in the extraction of terahertz (THz) wave radiation from a nonlinear crystal, where for example the THz radiation has been generated in the non-linear crystal through the process of parametric wave generation. FIG. 2(a) illustrates this, showing a coherent beam of electromagnetic radiation, referred to as the pump wave 4, used to stimulate a non-linear process in a non-linear optical material 5. This divides the energy/power of the coherent pump 4 into two newly generated parametric waves, typically referred to as the signal 6 and idler 7 waves. The signal wave is usually defined in the literature as the wave providing the useful output from the device, although that is not invariably the case. The ratio in which the pump energy/power is divided between the signal and idler waves is determined by phase-matching processes and is always subject to conservation of energy, where the energy of a pump wave photon is equal to the sum of the energies of the generated signal and idler wave photons.
Within these constraints, there is considerable interest in extending the spectral coverage of parametric devices. This is because they are often used as sources of coherent electromagnetic radiation in spectral regions either not covered by any other sources or where a single parametric-wave source is capable of replacing a number of sources that would otherwise be needed in order to provide the spectral coverage required. A serious limitation encountered in attempting to extend the spectral coverage of parametric generation to new regimes of the electromagnetic spectrum is the detrimental effect of absorption within the non-linear material of one or more of the three waves involved in the non-linear interaction. As a result the spectral coverage attainable with a particular parametric generation scheme is often determined by the onset of such absorption rather than by the non-linear or phase-matching characteristics of the non-linear material. Hence, it follows that elimination of such a restriction results in improved spectral coverage attainable through the parametric generation process.
One solution to the problem of absorption in the non-linear material is to employ a configuration of interacting waves such that the wave subject to excessive absorption exits the non-linear material as rapidly as possible after its generation. This wave is usually, but not invariably, the signal wave, and is usually, but not invariably, the wave with the longest wavelength of the three waves involved in the parametric process. Two principal methods for bringing this about have been identified. One of these is based on using non-collinear phase matching in such a way as to cause the wave subject to absorption, which as previously stated is usually the wanted signal wave, to rapidly walk out from the non-linear material in a direction that is substantially lateral to the propagation direction of the pump wave, as shown in FIG. 2(b).
In FIG. 2(b), the wavelength of the signal wave is substantially different from the wavelength of the pump wave and the idler wave is close to being collinear with the pump wave. Hence, the propagation direction of the signal wave is substantially lateral to the propagation direction of the idler wave as well as the pump wave.
Examples of this technique are described in the articles “Efficient, tunable optical emission from LiNbO3 without a resonator”, by Yarborough et al, Applied Physics Letters 15(3), pages 102-4 (1969); “Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler”, by Kawase et al, Applied Physics Letters 68(18), pages 2483-2485 (1996); and “Terahertz wave parametric source”, by Kawase et al, Journal of Physics D: Applied Physics 35(3), pages R1-14 (2002), the contents of which are incorporated herein by reference.
FIG. 2(c) illustrates the phase-matching process for FIG. 2(b) through a so-called k-vector diagram where kp, ki, ks are the wave vectors of the pump, idler and signal respectively within the non-linear material 5, angle e is the angle subtended by the pump 4 and idler 7 waves and angle φ the angle subtended by pump wave 4 and signal wave 6. A difficulty with this approach is the extraction of the signal (THz) wave through the non-linear crystal to air interface, due to the previously described effect of total internal reflection. It is usual that the angle of incidence the signal wave makes with this interface is greater than that for which total internal reflection is observed.
One known approach, as described for example by Kawase et al, Applied Optics 40(9), pages 1423-1426 (2001), to avoid reflection at the non-linear crystal to air interface is to apply to the interface a device fabricated from the semi-insulator material silicon, this having a intermediate refractive index (n3) of around 3.2, so that the total internal reflection condition (α) at the now non-linear crystal to silicon device interface is greater than the THz (signal) wave angle of incidence. Thus, the THz wave propagates through the interface, albeit with some loss due to Fresnel reflection.
If a silicon device having a second surface opposite and parallel to the first non-linear crystal to silicon interface surface is used, the problem of total internal reflection would be translated to this silicon to air interface. With reference to FIG. 3(a), the silicon device 9 used is prismatic in form, having a silicon to air interface 12 angled to the first interface 11 such that the THz wave in the silicon impinges the silicon to air interface 12 at an angle that is near normal to the plane of the face, hence less than the total internal reflection angle for this interface, and so transmitted through the silicon to air interface 12, but again subject to a Fresnel reflection loss.
A problem with the use of silicon in THz devices is that free carriers can be created when the material is subject to illumination by light at a frequency higher or wavelength shorter than the material band-gap, which in the case of silicon is around 1 micron in wavelength. To limit the effects of stray light, as shown in FIG. 3(b), a screen 13 has been used, described for example by Kawase et al, Applied Optics 40(9), pages 1423-1426 (2001). Here the screen 13 is positioned so that it prevents pump wave light from impinging the prismatic silicon output of a coupling device that is applied to a MgO:LiNbO3 non-linear crystal. In this case, the pump wave light otherwise impinging the silicon prism arises from parasitic reflection from other optical components 14 within the THz parametric generation system.